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MathGroup Archive 2000

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Confluent hypergeometric functions of matrix argument

  • To: mathgroup at
  • Subject: [mg24552] Confluent hypergeometric functions of matrix argument
  • From: Matthew Antone <tone at MIT.EDU>
  • Date: Mon, 24 Jul 2000 03:04:31 -0400 (EDT)
  • Organization: MIT Computer Graphics Group
  • Sender: owner-wri-mathgroup at


I'm looking for some code (preferably C, but FORTRAN or pseudocode for
an algorithm would also be good) to compute the confluent hypergeometric

function of matrix argument, 1F1(a; b; M).

I only need to evaluate a specialized case, namely 1F1(0.5; 1.5; D)
where D is a real diagonal 3x3 matrix. One of the diagonal elements of D

is always 0, and the other two are arbitrary real values.

I've seen various implementations of 1F1 for scalar arguments on netlib
and other areas but I don't think they can be used for my problem.

Ideally I'd like code to compute the above values of 1F1 (or the
logarithm of these values) and also perhaps code to take first and
second derivatives of 1F1 or of log(1F1) with respect to the matrix
parameters in D.

Any help would be greatly appreciated. Please respond to tone at
and/or post a response to this group if you have any leads.

Thanks very much,

    - Matt

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